Estimates of school productivity and implications for policy

School productivity was not perfectly estimated because of the sampling error and the measurement error. The traditional Ordinary Least Square (OLS) leaves the estimation of school productivity questionable. Moreover, Hierarchical Linear Model (HLM) encounters a large proportion of the variance unexplained in the level-1 equation. In the paper, I will first introduce the Kalman Filter (KF) algorithm together with the Bayesian random draw mechanism to simulate the accurate school effects, and then compare the simulated results with the estimates generated from OLS and HLM. The comparison of the school effects will conclude that the Kalman Filter is more reliable and accurate for the educators and school administrators to supervise the allocation of the school resources for school improvement. Introduction The current focus of American K-12 education is to raise students’ academic performance. When we look back, American K-12 education has endured many changes, and the investment per student has increased in the past four decades. Within the school, data show that class size gets smaller. Most of the states have experienced the increasing teacher-pupil ratio since 1960s. In addition, the spending per student in K-12 education increased remarkably. However, student performance was stagnating, and concern about education quality was intensely argued by the school teachers, principals, and students’ parents. The simple production theory uses student performance as a measure of output changes when putting educational inputs into a school. Will we increase spending in schools? Did we invest enough money to achieve the desired changes for student achievement? The more proper argument is that the spending in K-12 education is inefficient and misused by schools. In other words, the current educational policies are ineffective to raise the school quality, especially in increasing student test scores. In order to establish an effective educational policy for students’ academic performance, the economists should begin looking for the accurate estimate of the school effects within a school district and across multiple districts since schools affect student performance. When thinking of schooling as the investment for the human capital, we understand that the inputs the students have today will influence their future productivity. Generally speaking, education benefits students and economic growth. Two facts come out from the empirical study of labor economics. The first fact is that wage is strongly correlated with the student’s educational level. Another one is that China’s economy grew